Download spherical aberration

Theoretical Optical Performance
of an Equal Conic Intraocular
Lens and Comparison to
Spherical and Aspheric IOLs
Edwin J. Sarver, PhD
The author(s) acknowledge
financial interest in the subject
matter of this presentation.
Acknowledgement…
• Contributors on this project…
–
–
–
–
Don Sanders, MD, PhD
John Clough, LensTec
Hayden Beatty, LensTec
Jim Simms, LensTec
Background…
• Recent studies have shown that aspheric IOLs can
provide patients with significant optical benefits
over traditional spherical surface IOLs.
1: Altmann GE, Nichamin LD, Lane SS, Pepose JS. Optical performance of 3 intraocular
lens designs in the presence of decentration. J Cataract Refract Surg. 2005 Mar;31(3):574-85.
2: Bellucci R, Morselli S, Piers P. Comparison of wavefront aberrations and optical quality
of eyes implanted with five different intraocular lenses. J Refract Surg. 2004 JulAug;20(4):297-306.
3: Packer M, Fine IH, Hoffman RS, Piers PA. Improved functional vision with a modified
prolate intraocular lens. J Cataract Refract Surg. 2004 May;30(5):986-92.
4: Kershner RM. Retinal image contrast and functional visual performance with aspheric,
silicone, and acrylic intraocular lenses. Prospective evaluation. J Cataract Refract Surg. 2003
Sep;29(9):1684-94.
Optical benefits…
• The optical benefits are due to a reduction in
optical aberrations at the retina.
• Primarily, spherical aberration is reduced.
Spherical aberration
• Spherical aberration occurs when rays away
from the paraxial region do not intersect at the
paraxial focus.
Paraxial ray…
Paraxial ray
A paraxial ray is an optical ray traced “near”
the optical axis.
Paraxial focus…
Paraxial focus
Paraxial ray
The paraxial focus is where the paraxial ray
crosses the optical axis after refraction by the
lens.
Positive spherical aberration…
Off axis ray (positive sa)
Paraxial focus
Paraxial ray
When an off-axis ray is refracted by the lens
and crosses the axis in FRONT of the paraxial
focal point, the ray exhibits POSITIVE
spherical aberration.
Negative spherical aberration…
Off axis ray (positive sa)
Paraxial focus
Paraxial ray
Off axis ray (negative sa)
When an off-axis ray is refracted by the lens
and crosses the axis in BACK of the paraxial
focal point, the ray exhibits NEGATIVE
spherical aberration.
Corneal spherical
aberration…
• The mean corneal spherical aberration has been
reported to be about +0.27 microns1
• About 90% of the population has positive
corneal spherical aberration — About 10% of
the population has negative corneal spherical
aberration2
1Holladay
JT, et al, A new intraocular lens design to reduce spherical aberration of
pseudophakic eyes. J Refract Surg., 2002 Nov-Dec;18(6):683-91.
2Krueger
RR, et al, Wavefront Customized Visual Correction, Chapter 42, p. 368, 2004.
Approximate distribution of
corneal spherical aberrations
10% negative
90% positive
0.27 μm
Spherical IOLs
• A biconvex IOL with spherical surfaces exhibits
positive spherical aberration.
• Thus, usually, spherical IOLs ADD positive
spherical aberration to the already positive
corneal spherical aberration
Aspheric IOLs
• Aspheric IOLs attempt to improve pseudophakic
vision by controlling spherical aberrations
• One strategy is to design a lens with negative
spherical aberrations to balance the normally
positive corneal spherical aberrations
• Another strategy is to design a lens with
minimum spherical aberrations so that no
additional spherical aberration is added to the
corneal spherical aberrations
– Could be an asymmetric design
– Could be a symmetric design
Comparison of IOLs
• Given these IOL design strategies we want to
investigate their potential strengths and
weaknesses
• First, we will describe the designs…
22 D IOL designs…
Parameter
Spherical
Negative
surface IOL spherical
aberrations
Asymmetric
zero spherical
aberrations
Ref. index
1.427
1.458
1.427
R1
8.234
11.043
7.285
K1
0
-1.03613
-1.085667
4th & 6th coef
-0.000944,
R2
-8.234
-0.0000137
-11.043
-9.470
K2
0
0
-1.085667
Altmann, et al, Optical performance of 3 intraocular lens designs in the presence of
decentration, J Cataract Refract Surg. 2005;31(3):574-85.
22 D IOL design shapes…
Sphere
Spherical surface IOL
Propagation of light
Sphere
22 D IOL design shapes…
Sphere
Sphere
Spherical surface IOL
6th order asphere
Negative spherical
aberrations IOL
Propagation of light
Sphere
22 D IOL design shapes…
Sphere
Sphere
Spherical surface IOL
6th order asphere
Sphere
Conic
Conic
Negative spherical
aberrations IOL
Asymmetric zero
spherical aberrations IOL
Propagation of light
Equal conic, low spherical
aberrations IOL…
• Want to use conic surface for both anterior and
posterior
• Want both surfaces equal
• Want low spherical aberrations
Equal conic design
strategy…
n0 = 1.336
R
-R
Paraxial ray
F=1336 / P
First, we find the apical radius for the front and
back surfaces to give the desired power.
Equal conic design
strategy…
n0 = 1.336
Off axis ray
Paraxial ray
K
K
Next, we find the conic K parameter so that off
axis rays intersect the paraxial focus.
22 D IOL designs…
Parameter Sphere / 6th Order
Sphere asphere /
Sphere
Ref.
index
R1
K1
Conic 1 /
Conic 2
Equal
conic
1.427
1.458
1.427
1.4585
8.234
11.043
7.285
11.093
0
-1.03613
-1.085667
-1.23
-9.470
-11.093
-1.085667
-1.23
4th & 6th
coef
-0.000944,
R2
-8.234
-0.0000137
-11.043
K2
0
0
Longitudinal aberrations…
Negative spherical
aberration
Spherical
Note: spherical aberration in opposite directions.
Longitudinal aberrations…
Negative spherical
aberration
Negative spherical aberrations
Spherical
Positive spherical aberrations
Longitudinal aberrations…
Equal conic
Unequal conic
Note: scale is 1000 x smaller than previous slide.
More important…
• Rather than just look at the performance of the
IOL alone, it is more important to consider how
it performs in the eye.
• To facilitate this analysis, we use a simple
aspheric eye model.
Choice of eye model…
• Negative spherical aberration IOL was
optimized for anterior cornea K = -0.1414
• “Zero” spherical aberration IOLs work best with
anterior cornea with K = -1/n2 = -0.53
• Mean cornea has K = -0.26
• Kooijman1 eye model has K = -0.25, (we use
this model)
1Atchison
and Smith, Optics of the human eye, Butterworth-Heinemann,
2000, p.255.
Kooijman/optical model
R2=6.5,
K2=-0.25
R1=7.8,
K1=-0.25
n=1.3771
n=1.336
ELP=4.5
AL adjusted to give best focus for 3 mm pupil.
Centered performance…
Centered – 3 mm Pupil
MTF -- Centered 3MM Pupil
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
All IOLs work pretty well here – MTF is limited
by diffraction.
Centered – 5 mm Pupil,
K=-0.1414
MTF -- Centered 5 mm Pupil
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
This is where negative spherical aberration IOL
works best.
Centered, 5 mm Pupil,
K=-0.25
MTF -- Centered, 5 mm Pupil, Kooijman
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
As the eye model is adjusted, note how dramatically the
performance is modified.
Centered, 5 mm Pupil,
K=-0.53
MTF -- Centered, 5 mm Pupil, K=-0.53
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
When the cornea has spherical aberrations near zero, the
“zero” spherical aberration IOLs perform best.
Centered IOL observations…
• Over this range of K values, the spherical IOL is
has lowest performance
• The best performer in the group of conic surface
IOLs depends upon the K value
• For the mean K of -0.25, the negative spherical
aberration IOL performs best
Tilt…
10 deg tilt – 3 mm pupil,
K=-0.1414
MTF -- 10 deg Tilt, 3 mm Pupil
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
For this eye model, all IOLs perform about the same.
10 deg tilt, 3 mm pupil,
K=-0.25
MTF -- Tilt 10 deg, 3 mm Pupil, Kooijman
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
For mean corneal shape, the negative spherical
aberration IOL performance starts to fall off.
10 deg tilt, 5 mm pupil,
K=-0.1414
MTF -- 10 deg Tilt, 5 mm Pupil
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
CPD
Performance for all IOLs close again…
60.0
10 deg tilt, 5 mm pupil,
K=-0.25
MTF -- Tilt 10 deg, 5 mm Pupil, Kooijman
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
“Zero” spherical aberration IOLs start to perform better
for mean corneal shape.
Tilt observations…
• Depending upon the corneal eccentricity:
– The performance of the IOL designs are comparable
– For some cases, the zero spherical aberration IOLs
out perform the spherical surface and negative
spherical aberration IOLs
Decentration…
Decentration 1 mm,
3 mm pupil, K=-0.1414
MTF -- 1 mm Decenter, 3 mm Pupil
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
Clearly, the spherical surface and negative spherical aberrations
IOLs have trouble with decentration.
Decentration 1 mm,
3 mm pupil, K=-0.25
MTF -- Decenter 1mm, 3 mm Pupil, Kooijman
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
This trend does not depend upon the corneal shape factor.
Decentration 1 mm –
5 mm pupil, K=-0.1414
MTF -- 1 mm Decenter, 5 mm Pupil
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
The same optical behavior is seen for the 3 and 5 mm pupils.
Decentration 1 mm,
5 mm pupil, K=-0.25
MTF -- Decenter 1mm, 5 mm Pupil, Kooijman
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
Again, the same trend that does not depend upon corneal
eccentricity.
Decentration observations…
• For 1.0 mm decentration:
– The spherical surface and negative spherical
aberration IOLs do not perform as well as zero
aberration IOL designs
– The trends for decentration does not depend upon
pupil size or corneal eccentricity
Defocus…
Defocus 0.5D, 3 mm Pupil,
K=-0.1414
MTF -- Defocus 0.5D, 3 mm Pupil
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
For a 3 mm pupil, the corneal eccentricity does not affect optical
performance to a large degree – an seen in this and the next slide.
Defocus 0.5D, 3 mm Pupil,
K=-0.25
MTF --Defocus 0.5D, 3 mm Pupil, Kooijman
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
CPD
40.0
50.0
60.0
Defocus 0.5D, 5 mm Pupil,
K=-0.1414
MTF -- Defocus 0.5D, 5 mm Pupil
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
The general performance of the IOLs for 0.5D of defocus and 5 mm
pupil does not appear to depend upon corneal eccentricity.
Defocus 0.5D, 5 mm Pupil,
K=-0.25
MTF --Defocus 0.5D, 5 mm Pupil, Kooijman
1
0.9
0.8
Contrast
0.7
EC
0.6
UC
0.5
N
0.4
S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
As a side issue, the large ripples corresponding to the negative
spherical aberration IOL indicate regions of contrast reversal.
Defocus observations…
• For 0.5 D of defocus at 3.0 and 5.0 mm pupils,
the performance of all IOLs are about equal.
• The negative spherical aberration IOL shows
more contrast for low frequency objects than the
other IOLs
• The negative spherical aberration IOL showed
significant regions of contrast reversal at 5.0 mm
pupil
Closer look at EC & UC
• The equal conic IOLs and unequal conic IOL
designs appear to perform about the same
• Want to consider variability in tangential and
sagittal MTF components in more detail
Tilt of 10 deg, 5 mm pupil
MTF -- Tilt 10 deg, 5 mm pupil, Kooijman
1
0.9
0.8
Contrast
0.7
EC-T
0.6
EC-S
0.5
UC-T
0.4
UC-S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
The tangential and sagittal MTF components indicate a greater
variability for the unequal conic design compared to the equal conic
design.
Tilt |T-S| graph
MTF -- Tilt 10 deg, 5 mm pupil, Kooijman, |T-S|
0.45
0.4
Abs( T-S) Contrast
0.35
0.3
0.25
EC-Diff
0.2
UC-Diff
0.15
0.1
0.05
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
The magnitude of the differences between the tangential and sagittal
MTF components clearly show more variability for the unequal conic
design.
Decentration
MTF -- Decenter 1mm, 5 mm pupil, Kooijman
1
0.9
0.8
Contrast
0.7
EC-T
0.6
EC-S
0.5
UC-T
0.4
UC-S
0.3
0.2
0.1
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
It is more subtle which lens design is more variable.
Decentration |T-S| graph
MTF -- Decenter 1mm, 5 mm pupil, Kooijman, |T-S|
0.12
Abs( T-S ) Contrast
0.1
0.08
EC-Diff
0.06
UC-Diff
0.04
0.02
0
0.0
10.0
20.0
30.0
40.0
50.0
60.0
CPD
By comparison of the magnitude of the difference between tangential
and sagittal MTF, we see that the equal conic design has less
variability.
Discussion
• There are various conditions in which one IOL
design will perform better than another, but
generally…
– Aspheric IOLs perform better than spherical surface
IOLs
– For the level of alignment errors investigated here,
zero spherical aberration IOLs perform better than
spherical surface IOLs and negative spherical
aberration IOLs
Discussion…
• Recognizing the variability in corneal
eccentricity, it may be prudent to decide upon
the use of an aspheric IOL design as a function
of measured corneal aberrations (not ocular
aberrations)
• This IOL selection strategy was suggested by
Krueger et al.
Krueger RR, et al, Wavefront Customized Visual Correction, Chapter 42, p. 368, 2004.
Summary
• Aspheric IOLs have optical advantages over
spherical IOLs
• For small alignment errors and positive spherical
aberration corneas, negative spherical aberration
IOLs perform best
• For larger alignment errors, “zero” spherical
aberration IOLs perform best
Summary
• “Zero” spherical aberration IOLs perform well
over a wider range of corneal shapes and
alignment errors than negative spherical
aberration IOLs
• The equal and unequal conic IOL designs
perform are very similar
• The equal conic IOL design performs slightly
better than the unequal conic IOL design in
terms of smaller variability in tangential and
sagittal MTF components
Thank you!